Rectangle

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1. Diagonal 20
   Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
2. Trapezoid MO
   The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
3. Diamond diagonals
   Calculate the diamond's diagonal lengths if its content is 156 cm² and the side length is 13 cm.
4. TV transmitter
   The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
5. Store
   One meter of the textile were discounted by 2 USD. Now 9 m of textile cost as before 8 m. Calculate the old and new price of 1 m of the textile.
6. Motion
   If you go at speed 5.1 km/h, you come to the station 37 minutes after leaving train. If you go by bike to the station at speed 28 km/h, you come to the station 38 minutes before its departure. How far is the train station?
7. Sphere from tree points
   Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
8. Pool
   If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately?
9. Two pumps
   Pump A takes twice as long to fill a tank than B . Together they take 2 hours to fill the tank. How long does each one take to fill the tank by itself?
10. Supermarket 2
    A supermarket had a buko pie sale. In the morning 2/3 of the pies were sold and in the afternoon 1/6 of the pies were sold. If 150 pies were left, how many pies had been sold? Show your solution.
11. Gasoline tank 2
    A gasoline tank is 1/6 full. When 25 liters of gasoline were added, it became 3/4 full. How many liters more is needed to fill it? Show your solution.
12. Forestry workers
    In the forest is employed 43 laborers planting trees in nurseries. For 6 hour work day would end job in 35 days. After 11 days, 8 laborers go forth? How many days is needed to complete planting trees in nurseries by others, if they will work 10 hours a da
13. Excavation
    Mr. Billy calculated that excavation for a water connection dig for 12 days. His friend would take 10 days. Billy worked 3 days alone. Then his friend came to help and started on the other end. On what day since the beginning of excavation they met?
14. Coffee
    In stock are three kinds of branded coffee prices: I. kind......248 Kč/kg II. kind......134 Kč/kg III. kind.....270 Kč/kg Mixing these three species in the ratio 10:7:7 create a mixture. What will be the price of 1100 grams of this mixture?
15. Stamps 2
    Dennis spent 34.15 on stamps. The number of .56 is 10 less than four times of stamps bought for .41. How many of each stamp did he buy?
16. Parking
    At a building parking, 245 spaces are for cars, 56 are for vans and the rest are for buses. If 14% of all parking spaces are for buses, how many parking spaces are there in the building? How many spaces are for buses?
17. Inverse matrix
    Find out inverse by Gauss elimination or by reduction method. A=[2/3. 1 -3. 1/3]